Differential Geometry

Catalog description

Riemannian metrics, covariant derivatives, Gauss curvature, Riemann curvature; Gauss-Bonnet theorem; Exponential map and normal coordinates; The Hopf-Rinow Theorem; Jacobi fields; The Cartan-Hadamard Theorem; Ricci curvature and Myers' and Bonnet's Theorems; selected topics and K hler geometry; symplectic topology; gauge theory.